Poisson transforms for differential forms
Archivum Mathematicum (2016)
- Volume: 052, Issue: 5, page 303-311
- ISSN: 0044-8753
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topHarrach, Christoph. "Poisson transforms for differential forms." Archivum Mathematicum 052.5 (2016): 303-311. <http://eudml.org/doc/287527>.
@article{Harrach2016,
abstract = {We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite dimensional representations of reductive Lie groups. Moreover, we will explicitly generate a family of degree-preserving Poisson transforms whose restriction to real valued differential forms has coclosed images. In addition, as a transform on sections of density bundles it can be related to the classical Poisson transform, proving that we produced a natural generalization of the classical theory.},
author = {Harrach, Christoph},
journal = {Archivum Mathematicum},
keywords = {Poisson transforms; integral transform of differential forms; homogeneous spaces},
language = {eng},
number = {5},
pages = {303-311},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Poisson transforms for differential forms},
url = {http://eudml.org/doc/287527},
volume = {052},
year = {2016},
}
TY - JOUR
AU - Harrach, Christoph
TI - Poisson transforms for differential forms
JO - Archivum Mathematicum
PY - 2016
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 052
IS - 5
SP - 303
EP - 311
AB - We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite dimensional representations of reductive Lie groups. Moreover, we will explicitly generate a family of degree-preserving Poisson transforms whose restriction to real valued differential forms has coclosed images. In addition, as a transform on sections of density bundles it can be related to the classical Poisson transform, proving that we produced a natural generalization of the classical theory.
LA - eng
KW - Poisson transforms; integral transform of differential forms; homogeneous spaces
UR - http://eudml.org/doc/287527
ER -
References
top- Čap, A., Slovák, J., Parabolic geometries I – Background and general theory, AMS, 2009. (2009) Zbl1183.53002MR2532439
- Gaillard, P.-Y., 10.1007/BF02621934, Comment. Math. Helv 61 (4) (1986), 581–616, (French). (1986) Zbl0636.43007MR0870708DOI10.1007/BF02621934
- Greub, W., Halperin, S., Vanstone, R., Connections, curvature, and cohomology, vol. I, Academic Press, 1972. (1972) Zbl0322.58001
- Helgason, S., Groups and geometric analysis. Integral geometry, invariant differential operators and spherical functions, Pure Appl. Math. (1984). (1984) Zbl0543.58001MR1790156
- Helgason, S., Geometric analysis on symmetric spaces, Mathematical Surveys and Monographs, vol. 39, AMS, 1994. (1994) Zbl0809.53057MR1280714
- Thurston, W., The geometry and topology of three manifolds, Lecture Notes, available online: http://library.msri.org/books/gt3m.
- van der Ven, H., 10.1006/jfan.1994.1015, J. Funct. Anal. 119 (1994), 358–400. (1994) Zbl0813.53034MR1261097DOI10.1006/jfan.1994.1015
- Yang, A., Vector valued Poisson transforms on Riemannian symmetric spaces, Ph.D. thesis, Massachusetts Institute of Technology, 1994. (1994)
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